The invention relates to a birefringence distribution measuring method, and, more particularly, it concerns such a method which obtains quantitatively and two-dimensionally a birefringence distribution induced when thermal or mechanical stress is produced in a laser medium of a solid state laser represented by a YAG laser, for example.
A solid state laser, such as a YAG laser, begins laser oscillation when energy from an excitation light source, such as a lamp, is applied to a laser medium. A part of the lamp light is converted into heat and accumulated in the laser medium so that a temperature gradient or distortion is produced inside the laser medium. As is well known, this causes the laser medium to have optical anisotropy, thereby allowing birefringence to appear.
More particularly, when a temperature gradient is produced inside the laser medium, the difference in thermal expansion between the surface and the center of the medium makes the medium distort, thus generating internal stresses. Similarly, mechanical stresses resulting from mounting the laser medium causes internal stresses in the laser medium. The refractive index of a medium for light depends on stress. As a result, a distribution of refractive indices is produced inside the medium (photoelastic effect).
Also, the refractive index changes in accordance with the polarization direction of light. The refractive index in the direction of the principal axis is different from that of a direction perpendicular to the principal axis, so that when linearly polarized light enters a birefringent substance at an angle to the principal axis of stress produced in the substance, the phase velocities in the two directions are differentiated from each other. The resulting phase difference produces elliptically polarized light. Further, two light beams of different vibration directions progress in different velocities (birefringence) through the birefringent substance. Of the two polarized waves due to birefringence, one wave having one plane of vibration progresses more rapidly, and the other wave progresses slowly. The two waves are called "fast wave" and "slow wave", respectively.
In a solid state laser, a laser beam is amplified when it is reflected back and forth between two mirrors. When birefringence due to the thermal or mechanical stress has occurred inside the laser medium, therefore, the relative phase difference between the two refracted beams causes the wave front to be disturbed, thereby presenting an obstacle to effective laser operation in cases where a laser beam emitted from a laser is output as linearly polarized light and then amplified for use.
From the standpoint of promoting the study of birefringence compensation to obtain a laser beam having a small wave front distortion, therefore, there is a need for an improved method for measuring, two-dimensionally, a birefringence distribution which obtains quantitatively and with high sensitivity birefringence induced in a laser medium of a solid state laser.
Typically, known methods for quantitatively measuring a two-dimensional distribution of birefringence using a conoscope. FIGS. 3 and 4 show in block diagram from systems representing the principle of the known measuring method. In these figures, 1 designates a sample having a birefringence effect (e.g., a crystal plate or glass plate which is to be used as a laser medium of a solid state laser), 2 designates a monochromatic light source (e.g., He-Ne laser), 3 designates an optical receiver for guiding a received image to a screen, 4 designates a polarizer, 5 designates an analyzer, and 6 and 7 designate quarter-wave plates.
In FIG. 3, the sample 1 is placed between a circular polarizer (a combination of the polarizer 4 and the quarter-wave plate 6) and a circular analyzer (which is a combination of the quarter-wave plate 7 and the analyzer 5 and which is arranged to establish crossed Nicols with respect to the circular polarizer), and arranged in the optical path between the light source 2 and the optical receiver 3. In the configuration, monochromatic parallel beams emitted from the light source 2 are converted into circularly polarized light by the circular polarizer and then projected onto sample 1. The light beams which have undergone birefringence inside the sample 1 pass through the circular analyzer to be detected by the optical receiver 3. When the light intensity after passing through the polarizer 4 is I.sub.0, the light intensity detected by the optical receiver 3 is indicated by I, the angle of the axis at a point in the sample 1 which is formed by the vibration direction of the fast wave passing through the sample and the principal plane of the analyzer 5 is indicated by .phi., and the relative phase difference between the two beams due to birefringence is indicated by .delta., as is well known, the intensity distribution changes in proportion to the equation: EQU I=I.sub.0 sin.sup.2 (.delta./2) (1)
In the configuration of FIG. 4 which is the same as that of FIG. 3 except that the quarter-wave plates 6 and 7 are omitted, the intensity distribution changes in proportion to the equation: EQU I=I.sub.0 sin.sup.2 (2.phi.).times.sin.sup.2 (.delta./2) (2)
In the configuration of FIG. 4, therefore, the intensity distribution of the intensity of the beams passing through the sample 1 and detected by the optical receiver 3 is measured. The direction in which the intensity is zero (I=0) indicates the direction of the principal axis (angle .phi.). From the intensity to this direction, the relative phase difference 6 can be calculated in accordance with Eq. (2). In the configuration of FIG. 3, the information relating to the direction principal axis is lost, and therefore only the relative phase difference .delta. is obtained.
As seen from Eqs. (1) and (2) above, according to the birefringence distribution measuring method using a conoscope, it is possible to obtain the absolute value of the relative phase difference .delta. between two refracted beams due to birefringence, and also the two-dimensional distribution of birefringence, but it is impossible to determine the sign of the relative phase difference .delta.. Further, in Eqs. (1) and (2) above, the relative phase difference .delta. is presented in the term of a second degree, sin.sup.2 (.delta./2). Therefore, when the relative phase difference .delta. is very small, for example, less than .pi./4 radians, the term of sin.sup.2 (.delta./2) is approximated to be .delta..sup.2 /4, resulting in impaired measurement sensitivity.
As described above, the prior art measuring method cannot judge the sign of the relative phase difference .delta.. In the state of the art, a simple method of two-dimensionally measuring a birefringence distribution which can obtain both the sign of the relative phase difference and the principal axis direction has not yet been put to practical use.